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How does QM allow imaging of individual electron orbitals?

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Question: Why does the uncertainty principle allow probing of characteristics specific to the electron orbital distribution? If you measure an electron's position/momentum, then after you measure it, it is obviously no longer in that exact same orbital. What's going on?

Recently, a new AFM technique has allowed researchers to distinguish between different types of chemical bonds (paper link). The published results clearly distinguishes information about bonding electrons (specific to benzene structures).

What does quantum mechanics state about variability of measurement of electrons in coherent states? Must the orbitals be excited to get information about it? Do they then give off an emission in order to return to the ground state? If the electrons aren't actively disturbed in these processes, wouldn't that be a blatant violation of the uncertainty principle? What are the statistical limitations of getting information about an electron orbital? Theoretically, could you experimentally map the exact 3D wave function of an orbital?

I want this question to be agnostic to the method like AFM, although AFM seems particularly confusing to me. As I understand the idea, it moves a tip along a surface and detects slight movement as it moves over humps. You can imagine a single electron orbital as a hump and the probe moving over it continuously being pushed up or down due to the electrostatic attraction or repulsion. But this is clearly wrong! Such a process couldn't be smooth.

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2 Answers

Molecular orbitals (MOs) represent regions in a molecule where an electron is likely to be found

They are not a particle, the electron, they are a locus, thus the Heisenberg Uncertainty is irrelevant because they do not represent a single interaction.

They are probing the collective field of the molecular structure. They are working in the continuum with X rays which are not of the order of the quantum mechanical discrete spectra of the bound to the molecular structure electrons. There is continuum photon- molecule scattering and this is what they are probing.

As an analogue consider a simple potential well describing a system. There are the bound states and there is the continuum. When scattering with positive energy over the well resonances can be seen corresponding to the bound state available energies. The probes are working in a similar way.

@Shaktyai This seems to be a similar technique as AlanSE is discussing. It is continuum scattering and not excitations of specific bound states. Quantum mechanics has elastic scattering and Compton scattering etc which are not discrete bound state transitions.

My remark was just about this part of your answer: " They are working in the continuum with X rays which are not of the order of the quantum mechanical discrete spectra of the bound to the molecular structure electrons". In the paper valence electrons interact with Xrays.

@Shaktyai They call it a "wave mixing mechanism" and nowhere in the write up are they talking of transitions and/or disruptions of the lattice. It is a complicated scattering where part of the collective crystal energy is transfered to the X-ray beam. Nowhere does it say that the valence electrons change orbits.

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AFM measures a force which is more or less directly linked to the position of electrons or atoms. It does not measure both positions and momemtum, so it does not violate Heisenberg's uncertainty principle. And keep in mind that all the nice pics we see are computer generated.
I can't find the ref, but the interpretation of AFM pics where one sees atoms on a surface has been subjected to some controversy. Scientists were not so sure where to exactly locate the atoms.

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